Some smooth Finsler deformations of hyperbolic surfaces

Details Some smooth Finsler deformations of hyperbolic surfaces Some smooth Finsler deformations of hyperbolic surfaces

2007-04-23

arxiv.org/abs/0704.2927v1

Annals of Global Analysis and Geometry 35, 2 (2009) 191--226

Mathematics

Differential Geometry

Scientific paper

10.1007/s10455-088-9130-z

Given a closed hyperbolic Riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into Finsler metrics that are not Riemannian and whose properties are such that the classical Riemannian results about entropy rigidity, marked length spectrum rigidity and boundary rigidity all fail to extend to the Finsler category.

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